System and Method for Wireless Communications

ABSTRACT

A system and method for wireless communications is provided. A method for operating in a communications network includes receiving a codebook, the codebook includes a plurality of codewords, and determining if the codebook satisfies a constant modulus property. The method also includes in response to determining that the codebook does not satisfy the constant modulus property, converting the codebook into a codebook satisfying the constant modulus property, and storing the codebook satisfying the constant modulus property. The method further includes storing the codebook in response to determining that the codebook does satisfy the constant modulus property, and causing to transmit a transmission to a communications device, wherein the transmission is encoded using a codeword in the stored codebook.

This application is a continuation of U.S. patent application Ser. No.12/548,278, entitled “System and Method for Wireless Communications,”filed on Aug. 26, 2009 and U.S. Provisional Application No. 61/092,043,filed on Aug. 26, 2008, entitled “Modulus Normalization for the CodebookDesign,” which applications are hereby incorporated herein by reference.

TECHNICAL FIELD

The present invention relates generally to wireless communications, andmore particularly to a system and method for wireless communicationsusing a constant modulus (CM) codebook.

BACKGROUND

Communication system capacity generally may be significantly improvedwhen the transmitter has full or partial channel state information(CSI). CSI may be obtained by a transmitter via a reverse feedbackchannel between the transmitter and a receiver. To accommodate thelimited feedback channel bandwidth, CSI normally is quantized intodigital format at the receiver before being fed back to the transmitter.A codebook based algorithm generally is one of the most efficient waysto quantize the channel. A generic codebook may consist of multiplecodewords. In general, the codeword is selected based on certainselection criteria and the corresponding codeword index is fed back fromthe receiver to the transmitter. The principles for codeword selectionmay be varied based on different precoding techniques.

One of the challenges of the codebook design is the balance between thefeedback overhead and the quantization accuracy. Generally, the morecodewords included in a codebook, the better the channel quantizationaccuracy. The large number of codewords, however, also means largerfeedback load.

Another challenge of the codebook design is to cover a wide range ofchannel characteristics. For example, a correlated channel and anuncorrelated channel generally have very different properties and,therefore, come with different codebook design criteria.

Existing codebooks suffer significant challenges, however, includingshortcomings in performance for both correlated and uncorrelatedchannels, and complexity involved in codeword searching and differentialfeedback. What is needed, then, is a codebook and method of using sameto overcome these disadvantages in the prior art.

SUMMARY OF THE INVENTION

These and other problems are generally solved or circumvented, andtechnical advantages are generally achieved, by embodiments of a systemand method for wireless communications using a constant modulus (CM)codebook.

In accordance with an embodiment, a method for operating in acommunications network is provided. The method includes receiving acodebook, the codebook including a plurality of codewords, anddetermining if the codebook satisfies a constant modulus property. Themethod also includes in response to determining that the codebook doesnot satisfy the constant modulus property, converting the codebook intoa codebook satisfying the constant modulus property, and storing thecodebook satisfying the constant modulus property. The method furtherincludes storing the codebook in response to determining that thecodebook does satisfy the constant modulus property, and causing totransmit a transmission to a communications device. The transmission isencoded using a codeword in the stored codebook.

In accordance with another embodiment, a method for communicationsdevice operation in a communications network is provided. Thecommunications network having a base station. The method includescomputing an estimate of a communications channel between thecommunications device and the base station, quantizing the estimate witha first codebook, and transmitting information based on the quantizedestimate to the base station. The first codebook satisfies a constantmodulus property.

In accordance with another embodiment, a method for base stationoperation in a communications network is provided. The base stationserving a communications node. The method includes receiving channelinformation from the communications node, extracting a codebook indexfrom the channel information, reconstructing a channel estimate usingthe codebook index and a codebook, and causing to transmit atransmission to the communications node. The codebook satisfies aconstant modulus property, and the transmission is precoded using thereconstructed channel estimate.

An advantage of an embodiment is that the use of a CM codebook intransmissions may help to avoid transmit power imbalance in multipleinput, multiple output (MIMO) communications systems.

A further advantage of an embodiment is that the use of a CM codebookmay also reduce computational complexity by decreasing the number ofmultiplications required in signal processing. By reducing thecomputational complexity, the computation load may be decreased, whichmay allow for the use of computationally less powerful, lower powerconsuming, and less expensive computing hardware in a communicationsdevice.

The foregoing has outlined rather broadly the features and technicaladvantages of the present invention in order that the detaileddescription of the embodiments that follow may be better understood.Additional features and advantages of the embodiments will be describedhereinafter which form the subject of the claims of the invention. Itshould be appreciated by those skilled in the art that the conceptionand specific embodiments disclosed may be readily utilized as a basisfor modifying or designing other structures or processes for carryingout the same purposes of the present invention. It should also berealized by those skilled in the art that such equivalent constructionsdo not depart from the spirit and scope of the invention as set forth inthe appended claims.

BRIEF DESCRIPTION OF THE DRAWINGS

For a more complete understanding of the embodiments, and the advantagesthereof, reference is now made to the following descriptions taken inconjunction with the accompanying drawings, in which:

FIG. 1 is a diagram of a wireless communication system;

FIG. 2 a is a diagram of a prior art BTS;

FIG. 2 b is a diagram of a prior art subscriber unit;

FIG. 3 a is a diagram of a BTS;

FIG. 3 b is a diagram of a subscriber unit;

FIG. 4 is a flow diagram of operations in CM codebook generation;

FIG. 5 a is a diagram of a base codebook;

FIG. 5 b is a diagram of a localized codebook;

FIG. 5 c is a flow diagram of operations in adjusting a localizedcodebook;

FIG. 6 is a diagram of the hierarchical structure of the combinationcodebook;

FIG. 7 is a diagram of codeword searching for the combination codebookfor a MIMO wireless communications system with four transmit antennas;

FIG. 8 a is a data plot of system throughput for a range ofsignal-to-noise ratios for several different codebooks for a MIMOcommunications system with four transmit antenna and two receive antennaand a first traffic model;

FIG. 8 b is a data plot of system throughput for a range ofsignal-to-noise ratios for several different codebooks for a MIMOcommunications system with four transmit antenna and two receive antennaand a second traffic model;

FIGS. 9 a and 9 b are flow diagrams of subscriber unit operations ingenerating channel quality information feedback; and

FIGS. 10 a and 10 b are flow diagram of BTS operations in transmittinginformation to a subscriber unit using channel quality informationfeedback provided by the subscriber unit.

DETAILED DESCRIPTION OF ILLUSTRATIVE EMBODIMENTS

The making and using of the embodiments are discussed in detail below.It should be appreciated, however, that the present invention providesmany applicable inventive concepts that can be embodied in a widevariety of specific contexts. The specific embodiments discussed aremerely illustrative of specific ways to make and use the invention, anddo not limit the scope of the invention.

The embodiments will be described in a specific context, namely a singleuser (SU) wireless communications system with two (2), four (4), andeight (8) transmit antennas, i.e., SU-MIMO. The invention may also beapplied, however, to both SU-MIMO and multiple user (MU) MIMO wirelesscommunications systems with an arbitrary number of transmit and receiveantennas.

FIG. 1 illustrates a wireless communication system 100. Wirelesscommunications system 100 includes a base transceiver station (BTS) 101and a plurality of subscriber units 105, which may be mobile or fixed.BTS 101 and subscriber units 105 communicate using wirelesscommunications. BTS 101 has a plurality of transmit antennas 115 whilesubscriber units 105 have one or more receive antennas 110. BTS 101sends control information and data to subscriber units 105 through adownlink (DL) channel 120 while subscriber units 105 send controlinformation and data to BTS 101 through uplink (UL) channel 125.

In general, a BTS, such as BTS 101, may also be referred to as a basestation, a NodeB, and enhanced NodeB, and so forth. Similarly, asubscriber unit, such as subscriber units 105, may also be referred toas a mobile station, a user, a subscriber, a User Equipment, and so on.

Subscriber units 105 may send control information on UL channel 125 toimprove the quality of the transmission on DL channel 120. BTS 101 maysend control information on DL channel 120 for the purpose of improvingthe quality of uplink channel 125. A cell 130 is a conventional term forthe coverage area of BTS 101. It is generally understood that inwireless communication system 100 there may be multiple cellscorresponding to multiple BTSs.

FIG. 2 a illustrates a prior art BTS 101. Data 200, in the form of bits,symbols, or packets for example, destined for a plurality of subscriberunits being served may be sent to a scheduler 205, which may decidewhich subscriber units will transmit in a given time/frequencyopportunity. Scheduler 205 may use any of a wide range of knownscheduling disciplines in the literature including round robin, maximumsum rate, proportional fair, minimum remaining processing time, ormaximum weighted sum rate. Generally scheduling decisions are based onchannel quality information feedback 245 fed back from a plurality ofsubscriber units.

Data from subscriber units selected for transmission are processed bymodulation and coding block 210 to convert the data to transmittedsymbols. Modulation and coding block 210 may also add redundancy for thepurpose of assisting with error correction and/or error detection. Amodulation and coding scheme implemented in modulation and coding blockis chosen based in part on information about the channel qualityinformation feedback 245.

The output of modulation and coding block 210 may be passed to atransmit beamforming block 220, which maps the output (a modulated andcoded stream for each subscriber unit) onto a beamforming vector. Thebeamformed outputs are coupled to antennas 115 through RF circuitry,which are not shown. The transmit beamforming vectors are input from asingle user block 225 or a multi-user block 230.

Either beamforming for single user (subscriber unit) beamforming ormultiple user (subscriber unit) beamforming may be employed, asdetermined by switch 235, based on information from scheduler 205 aswell as channel quality information feedback 245. Part of eachsubscriber unit's channel quality information feedback includes an indexto a codeword in codebook 215, corresponding to quantized channelinformation. The modulation/coding and beamforming may be repeated forall scheduled subscriber units based on the output from scheduler 205.

An extract codeword block 240 produces the quantized channel stateinformation based on the index received from channel quality informationfeedback 245. Extract codeword block 240 may use the index to referencethe codeword from codebook 215. The output of extract codeword block 240is passed to switch 235 that forwards the information to either singleuser block 225 or multi-user block 230. Other information may also bepassed to these blocks, for example a signal-to-interference-plus-noiseratio (SINR) estimate may be passed to the multi-user block 230 toimprove its performance. Single user block 225 uses the output ofextract codeword block 240 as the beamforming vector for the selectedsubscriber unit. Other processing may also be applied, such asinterpolation in the case that orthogonal frequency divisionmultiplexing (OFDM) modulation is employed.

Multi-user block 230 combines the codeword from codebook 215 and otherinformation from multiple subscriber units to derive the transmitbeamforming vectors employed for each subscriber unit. It may use anynumber of algorithms widely known in the literature including zeroforcing, coordinated beamforming, minimum mean squared errorbeamforming, or lattice reduction aided precoding for example. Channelquality information feedback 245 may, for purposes of illustration, bein the form of quantized channel measurements, modulation, coding,and/or spatial formatting decisions, received signal strength, andsignal-to-interference-plus-noise measurements, and so forth.

FIG. 2 b illustrates a prior art subscriber unit 105. Subscriber unit105 may have one or a plurality of receive antennas 110, connectingthrough RF circuitry, not shown, to a receiver signal processing block250. Some of the key functions performed by receiver signal processingblock 250 may be channel estimation 255 and estimatesignal-to-interference-plus-noise ratio (SINR) block 260. Channelestimation block 255 uses information inserted into the transmit signalin the form of training signals, training pilots, or structure in thetransmitted signal such as cyclostationarity to estimate coefficients ofthe channel between BTS 101 and subscriber unit 105.

Channel state information is quantized in a codebook-based quantizationblock 265, which uses codebook 215 (the same codebook as codebook 215 ofFIG. 2 a) also available at BTS 101. The output of quantization block265 may be the index of a codeword in codebook 215 that best correspondsto the channel state information. For example, the vector in codebook215 that is closest to the estimated channel vector in terms of minimumsubspace distance may be chosen, or the vector from codebook 215 thatmaximizes the effective SINR may be selected. The index of the codewordis provided to generate channel quality information block 270, whichgenerates channel quality information feedback 245 from the index. Thechannel quality information feedback 245 may be used to aid schedulingand transmit beamforming, for example.

In prior art, the beamforming vector f_(u) ^(#) chosen at thetransmitter comes from a finite set of possible beamforming vectorsF={f₁, f₂, . . . , f_(N)}, the coefficients of which may be from anynumber of codebooks known in the literature including Grassmanniancodebooks, DFT codebooks, vector quantization codebooks, etc.

The size of the codebook is given by N and is sometimes given in bitslog₂N. Prior art considers codebooks of size around 6 bits. The receiverselects the index of the best vector from the codebook at the receiveraccording to any number of codeword selection criteria. For example,quantization block 265 may compute the optimum index as

$k_{u} = {\max\limits_{{n = 1},2,\ldots \mspace{14mu},N}{{H_{u}f_{n}}}}$

and this index is incorporated into channel quality information feedback245 by generate channel quality information message block 270. Inanother embodiment, quantization block 265 computes the dominant rightsingular vector of H_(u) as v then computes the optimum index as

$k_{u} = {\min\limits_{{n = 1},2,\ldots \mspace{14mu},N}{d\left( {v,f_{n}} \right)}}$

using a subspace distance like the chordal distance. BTS 101 thenextracts codeword block sets f_(u) ^(#)=f_(k) _(*) , basically the indexreceived on the feedback channel is used to generate the beamformingvector used for transmission.

Now consider one embodiment of the multiple user transmission mode. Forillustrative purposes suppose that M_(t)=2, M_(r)=1, and there are twosubscriber units a and b chosen by scheduler 205. Suppose the transmitbeamforming vectors are computed using the zero-forcing precodingmethodology (described in T. Yoo, N. Jindal, and A. Goldsmith,Multi-Antenna Downlink Channels with Limited Feedback and UserSelection, IEEE Journal Sel. Areas in Communications, Vol. 25, No. 7,pp. 1478-1491, September 2007, for example). The received signal atsubscriber unit a after matched filtering and sampling may be written as

y _(a) =H _(a) f _(a) ^(#) s _(a) +H _(a) f _(b) ^(#) s _(b) +v _(a)

where y_(a) is the M_(r)×1 received signal vector (where M_(r) is thenumber of receive antennas), H_(a) is the M_(r)×M_(t) channel matrix(where M_(t) is the number of transmit antennas at the BTS) between BTS101 and subscriber unit a, f_(a) ^(#) is the M_(t)×1 transmitbeamforming vector designed for subscriber unit a, f_(b) ^(#) is theM_(r)×1 transmit beamforming vector designed for subscriber unit b,s_(a) is the symbol sent to subscriber unit a, s_(b) is the symbol sentto subscriber unit b, and v_(a) is the additive noise vector atsubscriber unit a's receiver of dimension M_(r)×1.

A similar equation may be written for subscriber unit b and thisequation may naturally be generalized to more than two subscriber units.In the case of M_(r)=1 the subscriber unit, may employ the samequantization method as described in the previous case to find an indexfor the quantized channel state in quantization block 265. Unlike thesingle user case, however, the subscriber unit may also send additionalinformation like an estimate of the signal-to-interference-plus-noise(SINR) ratio that includes effects of quantization. The reason is thatbecause quantized channel state information is used, and there isresidual interference that should be accounted for. This may beestimated in generate channel quality information block 270 using anynumber of techniques known in the litereature.

BTS 101 uses the SINR information in scheduler 205 to select thesubscriber units for transmission and also to estimate theirtransmission rates for modulation and coding block 210. With zeroforcing precoding, multi-user block 230 may compute the transmitbeamforming vector by inverting the matrix [f_(a), f_(b)], andnormalizing the columns to produce the beamforming vectors [f_(a) ^(#),f_(b) ^(#)]. Because of the effects of residual interference, multiusersystems as is well known in the prior art (see for example Yoo. Et. al.)require large codebook sizes, i.e., N may be large (for example, on theorder of 4,096 or more). A major challenge is that it is very difficultto perform the quantization in quanitization block 265 and generate thereconstruction in extract codeword block 240 when the codebook size islarge. The problem is overcome in the embodiments.

FIG. 3 a illustrates a BTS 301. Data 200, in the form of bits, symbols,or packets for example, destined for a plurality of subscriber unitsbeing served are sent to a scheduler 205, which decides which subscriberunits will transmit in a given time/frequency opportunity. Data fromsubscriber units selected for transmission are processed by modulationand coding block 210 to convert to transmitted symbols and addredundancy for the purpose of assisting with error correction or errordetection. The modulation and coding scheme is chosen based in part oninformation about the channel quality information feedback 315.

The output of modulation and coding block 210 is passed to a transmitbeamforming block 220, which maps the modulated and coded stream foreach subscriber unit onto a beamforming vector. The beamformed outputsare coupled to antennas 115 through RF circuitry. The transmitbeamforming vectors are input from single user block 225 or multi-userblock 230. Either beamforming for a single user or multi-userbeamforming may be employed, as determined by switch 235, based oninformation from scheduler 205 and channel quality information feedback315. Part of each subscriber units' channel quality information feedbackincludes a new progressive feedback message that provides indicescorresponding to progressively quantized channel information asdescribed in the embodiments.

Progressive reconstruction block 302 uses the indices in channel qualityinformation feedback 315 combined with a base codebook 305 and alocalized codebook 310 to reconstruct a high-resolution estimate of thequantized channel state information. The output of progressivereconstruction block 302 is passed to switch 235 that forwards theinformation to either the single user block 225 or the multi-user block230. Other information may also be passed to these blocks, for example aSINR estimate may be passed to the multi-user block 230 to improve itsperformance. Single user block 225 uses the output of progressivereconstruction block 302 as the beamforming vector for the selecteduser.

Multi-user block 230 combines the codeword and other information frommultiple users to derive the transmit beamforming vectors employed foreach subscriber unit. It may use any number of algorithms known in theliterature including zero forcing, coordinated beamforming, minimum meansquared error beamforming, or lattice reduction aided precoding, forexample.

Scheduler 205 may use any of the known scheduling disciplines in theliterature including round robin, maximum sum rate, proportional fair,minimum remaining processing time, or maximum weighted sum rate;generally scheduling decisions are based on channel quality informationfeedback 315 received from the plurality of subscriber units. Scheduler205 may decide to send information to a single subscriber unit viatransmit beamforming or may decide to serve multiple subscriber unitssimultaneously through multiuser MIMO communication.

Modulation and coding block 210 may perform any number of coding andmodulation techniques including quadrature amplitude modulation, phaseshift keying, frequency shift keying, differential phase modulation,convolutional coding, turbo coding, bit interleaved convolutionalcoding, low density parity check coding, fountain coding; or blockcoding. The choice of modulation and coding rate in a preferredembodiment is made based on channel quality information feedback 315 ina preferred embodiment and may be determined jointly in the scheduler205.

While not explicitly illustrated, it is obvious to those of ordinaryskill in the art that OFDM modulation can be used. Further, any numberof multiple access techniques could be used including orthogonalfrequency division multiple access; code division multiple access;frequency division multiple access; or time division multiple access.The multiple access technique may be combined with the modulation andcoding block 210 or the transmit beamforming block 220 among others.

Although the discussion focuses progressive reconstruction block 302 andthe use of base codebook 305 and localized codebook 310, it is obviousto those of ordinary skill in the art that BTS 301 may also use a singlecodebook in place of multiple codebooks (base codebook 305 and localizedcodebook 310) without modification. For example, progressivereconstruction block 302 may use an index in channel quality informationfeedback 315 with just base codebook 305 to reconstruct an estimate ofthe quantize channel state information. The output of progressivereconstruction block 302 is passed to switch 235 that forwards theinformation to either the single user block 225 or the multi-user block230. The remainder of BTS 301 may be as described above.

Channel quality information feedback 315 may, for purposes ofillustration, be in the form of quantized channel measurements,modulation, coding, and/or spatial formatting decisions, received signalstrength, and signal-to-interference-plus-noise measurements.

FIG. 3 b illustrates subscriber unit 303. Subscriber unit 303 may haveone or more receive antennas 110, connecting through RF circuitry to areceiver signal processing block 250. Some of the key functionsperformed by receiver signal processing block 250 include channelestimation block 255, estimate SINR block 260, and a mobility estimateblock 325.

Channel state information is quantized using a progressive quantizationblock 330 as described in the embodiments. Progressive quantizationblock 330 first quantizes the received signal to a base codebook 305then generates at least one successive refinement using a localizedcodebook 310. With each progressive refinement, localized codebook 310becomes more localized resulting in a more efficient quantization. Anindex from the base codebook and several indices from the localizedcodebook are output from progressive quantization block 330. An estimateof the amount of channel variation, produced by mobility estimate block325, may be used to improve the progressive quantization algorithm byinitializing the algorithm from a previous quantization level oradjusting the amount of localization.

Progressive feedback block 335 generates a new feedback message bycombining the base and localized codebook indices output fromprogressive quantization block 330. Generate channel quality informationblock 340 generates a special feedback control message employing theoutputs of progressive feedback block 335 to produce channel qualityinformation feedback 315.

Channel estimation block 255 may employ any number algorithms known inthe art including least squares, maximum likelihood, maximum a postiori,Bayes estimator, adaptive estimator, or a blind estimator. Somealgorithms exploit known information inserted into the transmit signalin the form of training signals, training pilots, while others usestructure in the transmitted signal such as cyclostationarity toestimate coefficients of the channel between the BTS and the subscriberunit.

Estimate SINR block 260 outputs some measure of performancecorresponding to the desired signal. In one embodiment this consists ofa received signal power to interference plus noise estimate. In anotherembodiment, it provides an estimate of the received signal-to-noiseratio. In yet another embodiment, it provides an estimate of the averagereceived signal power, averaged over subcarriers in an OFDM system.

Although the discussion focuses on progressive quantization block 330and the use of base codebook 305 and localized codebook 310, it isobvious to those of ordinary skill in the art that subscriber unit 303may also use a single codebook in place of multiple codebooks (basecodebook 305 and localized codebooks 310) without modification. Forexample, progressive quantization block 330 may quantize the receivedsignal to only base codebook 305. Progressive quantization block 330 mayoutput an index from base codebook 305. Progressive feedback block 335generates a new feedback message from only the index of base codebook305. Operation of subscriber unit 303 may continue as described above.

In general, codebook(s) for use in wireless communications systems withtwo (2), four (4), and eight (8) transmit antennas should be designedand selected based on performance, complexity, and a number of desirableproperties, including:

-   -   Performance—with a fixed amount of feedback (typically in bits),        the overall system throughput as well as average throughput for        individual communications devices should be good to excellent        for a wide range of communications channel conditions (including        uncorrelated, correlated, and dual-polarized).    -   Complexity—a) with a fixed amount of feedback, it may be desired        that the codebook design minimizes the amount of codebook        searching, and b) a codebook with the constant modulus (CM)        property may be desired to avoid (or reduce) the use of matrix        multiplications.    -   Power amplifier balance—a codebook with the CM property may be        desired to avoid (or reduce) transmission power imbalance.    -   Feedback overhead—a codebook design that supports differential        feedback to reduce overall feedback overhead may be desired.    -   Flexibility to extend to other MIMO scenarios—a codebook design        should cover both SU-MIMO and MU-MIMO, which typically requires        different sizes of codebooks.

As discussed above, a codebook with the CM property (simply, a CMcodebook) may help to avoid transmit power imbalance in MIMO wirelesscommunications systems as well as reduce computational complexity byreducing (or eliminating) the use of matrix multiplications. However,many well-known codebook design criteria, such as, Grassmannian linkpacking and progressive codebook design, may not always be able tocreate a CM codebook.

FIG. 4 illustrates a flow diagram of operations 400 in CM codebookgeneration. Operations 400 may be indicative of operations taking placein a codebook generator and the resulting CM codebook(s) may be storedin BTS and subscriber units for subsequent use. Alternatively,operations 400 may occur in a processing unit of a BTS to create CMcodebook(s) for use by the BTS and subscriber units served by the BTS.Operations 400 may occur to generate the CM codebook(s) and may berepeated if a need for additional CM codebook(s) arises.

Operations 400 may begin with the codebook generator receiving acodebook (or codebooks) (block 405). The codebook may have been stored,in a memory or some other storage media, for example, and retrieved forprocessing. For example, the codebook generator may have generated thecodebook in an earlier operation.

The codebook generator may then perform a check to determine if thecodebook has the CM property (block 410). Let the codebook berepresented as:

C={c _(i,j) }, iε[1, . . . ,N _(t) ]; jε[1, . . . ,N],

where N_(t) denotes the number of transmit antennas and N represents thenumber of codewords in the codebook. Consequently, C_(i,j) is the i-thelement of the j-th codeword.

The codebook may have the CM property if for each C_(i,j),

${c_{i,j}}^{2} = {\frac{1}{N_{t}}.}$

Conversely, if

${c_{i,j}}^{2} \neq \frac{1}{N_{t}}$

for one C_(i,j) then the codebook does not have the CM property.

If the codebook does not have the CM property, then it is possible toconvert the codebook so that it does have the CM property by normalizingthe codewords in the codebook (block 415). The normalized codebook maybe expressed as:

Ĉ={ĉ _(i,j) }, iε[1, . . . , N _(t) ]; jε[1, . . . ,N],

where

${\hat{c}}_{i,j} = {\frac{c_{i,j}}{c_{i,j}}.}$

After normalizing each codeword in the codebook to convert the codebookinto a codebook with the CM property or if the codebook already has theCM property, the codebook generator may store the codebook (i.e., theconverted codebook or the original codebook that is already CM) to amemory or some other storage media for subsequent use (block 420).Operations 400 may then terminate.

As described previously, wireless communications system 100 may make useof progressive quantization and progressive reconstruction inconjunction with a base codebook and one or more localized codebooks tohelp improve the overall performance of wireless communications system100. The base codebook and/or the localized codebooks may have the CMproperty to help reduce power amplifier imbalance and computationalrequirements.

The base codebook and the localized codebook may be collectivelyreferred to as a combination codebook. The combination codebookcomprises the base codebook and at least one localized codebook. Thelocalized codebook may be refined over multiple stages to produceadditional localized codebook. At least the base codebook may have theCM property. However, it may be preferred that the localized codebook(s)also have the CM property.

FIG. 5 a illustrates a representative example of a base codebook andFIG. 5 b illustrates a representative example of a localized codebook.In both FIGS. 5 a and 5 b, the codewords of the respective codebooks areillustrated as points, such as points 505, on a unit sphere 500. FIGS. 5a and 5 b illustrate the relationship between the base codebook and thelocalized codebook.

A base codebook may be selected depending on various design criteria.For example, in an uncorrelated MIMO channel, a discrete Fouriertransform (DFT) matrix is one of several good options in that a minimumchordal distance between codewords is maximized. A base codebook may bedefined as:

C _(base) ^(M) =[c _(base) ¹ ,c _(base) ² , . . . ,c _(base) ^(M)],

where M denotes the number of codewords in the base codebook.

A localized codebook, as shown in FIG. 5 b, may not be uniform. With theprocessing (including scaling and rotating) of the localized codebook,elements in the localized codebook may be interpreted as a satellitecodeword of the base codebook. A localized codebook may be defined as aN_(t)'N matrix expressible as:

C _(local) ^(N) =[c _(local) ¹ ,c _(local) ² , . . . ,c _(local) ^(N)],

where N_(t) is the number of transmit antenna, and N denotes the numberof codewords in the localized codebook. A centroid 510 of the localizedcodebook may be expressed as:

c _(cnt)=[1,0 , . . . ,0]_(1×N) ^(H).

According to a preferred embodiment, the localized codebook may have aconstraint that centroid 510 has equal chordal distance from eachcodeword in C_(local) ^(N). As a result, the localized codebook may berewritten as:

${C_{local}^{N} = \begin{bmatrix}{r\; ^{{j\theta}_{11}}} & {r\; ^{{j\theta}_{12}}} & \ldots & {r\; ^{{j\theta}_{1\; N}}} \\{r_{21}^{{j\theta}_{21}}} & {r_{22}^{{j\theta}_{22}}} & \ldots & {r_{2\; N}^{{j\theta}_{2\; N}}} \\\vdots & \vdots & \ddots & \vdots \\{r_{N_{t}1}^{{j\theta}_{N_{t}1}}} & {r_{N_{t}2}^{{j\theta}_{N_{t}2}}} & \ldots & {r_{N_{t}N}^{{j\theta}_{N_{t}N}}}\end{bmatrix}},$

in which it is given that

${{{\sum\limits_{i = 2}^{N_{t}}\; {r_{ij}}^{2}} + {r}^{2}} = 1},$

jε{1, . . . , N} and the distance between centroid 510 and the codewordsin the localized codebook is √{square root over (1−r²)}.

Since a single localized codebook may be used in conjunction with thebase codebook, it may be necessary to adjust the localized codebookbased on the codeword of the base codebook being used. FIG. 5 cillustrates a flow diagram of operations 550 in adjusting the localizedcodebook. Operations 550 may be indicative of operations taking place ina subscriber unit as it generates a progressive quantization of channelstate information derived from a received signal transmitted by the BTS.Operations 550 may also be indicative of operations taking place in aBTS as it uses progressive reconstruction to reconstruct the codewordsfrom the indices of the base codebook and the localized codebookprovided by the subscriber unit. Operations 550 may occur each time thesubscriber unit performs a channel estimation to provide channelfeedback information to the BTS or when the BTS receives channelfeedback information from the subscriber unit.

Operations 550 may begin with a scaling of the localized codebook (block555). The chordal distance between centroid 510 and the codewords of thelocalized codebook may be scaled to accommodate various operationscenarios. In a situation when the chordal distance is to be scaled to avalue of α√{square root over (1−r²)}, the scaled version of thelocalized codebook is expressible as:

${{C_{local}^{N}(\alpha)} = \begin{bmatrix}\sqrt{\begin{matrix}{1 - \alpha^{2}} \\{\left( {1 - r^{2}} \right)^{{j\theta}_{11}}}\end{matrix}} & \sqrt{\begin{matrix}{1 - \alpha^{2}} \\{\left( {1 - r^{2}} \right)^{{j\theta}_{12}}}\end{matrix}} & \ldots & \sqrt{\begin{matrix}{1 - \alpha^{2}} \\{\left( {1 - r^{2}} \right)^{{j\theta}_{1\; N}}}\end{matrix}} \\{\alpha \; r_{21}^{{j\theta}_{21}}} & {\alpha \; r_{22}^{{j\theta}_{22}}} & \ldots & {\alpha \; r_{2\; N}^{{j\theta}_{2\; N}}} \\\vdots & \vdots & \ddots & \vdots \\{\alpha \; r_{N_{t}1}^{{j\theta}_{N_{t}1}}} & {\alpha \; r_{N_{t}2}^{{j\theta}_{N_{t}2}}} & \ldots & {\alpha \; r_{N_{t}N}^{{j\theta}_{N_{t}N}}}\end{bmatrix}},$

where α is the scaling factor.

Operations 550 may also include codeword rotation (blocks 560 and 565).Blocks 560 and 565 may be collectively referred to as codeword rotation(block 570). Codeword rotation (block 570) may involve rotating vectorc_(cnt) to the codeword c_(base) ^(m) in the base codebook, where mε{1,. . . , M}. By doing so, the localized codebook may also be rotated tosurround c_(base) ^(m). As a result, centroid 510 of the rotatedlocalized codebook becomes the codeword c_(base) ^(m). Specifically, thecodeword rotation may be performed in a multi-stage process.

A first stage of the codeword rotation (block 560) may involve finding arotation matrix R^(m), by which vector c_(cnt) may be rotated to vectorc_(base) ^(m). The rotation matrix R^(m) may be any unitary matrix witha constraint of (R^(m))^(H)c_(base) ^(m)=c_(cnt). It may be obvious thatR^(m)c_(cnt)=c_(base) ^(m), which indicates that vector c_(cnt) has beenrotated to vector c_(base) ^(m).

A second stage of codeword rotation (block 565) may involve rotating thelocalized codebook C_(local) ^(N) by the rotation matrix R^(m). Therotated localized codebook may be denoted

C _(local) ^((N,m)) =R ^(m) C _(local) ^(N).

Operations 550 may then terminate.

The combination codebook, denoted CX^(N) ^(t) ^(,r), where X=M×N denotesthe side of the combination codebook and r is the rank, may be obtainedbased on the scaled and rotated localized codebooks. CX^(N) ^(t) ^(,r)may be an N_(t)×(MN)-sized matrix and may be expressed as:

CX ^(N) ^(t) ^(,r) =[C _(local) ^((N,1)) , C _(local) ^((N,2)) , . . .,C _(local) ^((N,M))].

In various deployment scenarios (e.g., MU-MIMO and SU-MIMO), therequired quantization accuracy (or the size of the codebook) may vary.As a result, the combination codebook CX^(N) ^(t) ^(,r) may be furtherrefined. Specifically, CX^(N) ^(t) ^(,r) may be used as a base codebook.Then, with predefined scaling factors and a localized codebook, a newcodebook may be readily obtained using the above discussed techniques.

FIG. 6 illustrates a hierarchical structure of the combination codebook.As shown in FIG. 6, N_(i) represents the localized codebook sizeassociated with an i-th layer (refinement). The inherent hierarchicalstructure of the combination codebook may both simplify the searchingfor codewords as well as differential feedback.

Codeword searching may be simplified by the hierarchical structure ofthe combination codebook. Specifically, in a layer, only the nodes whichare associated with the selected nodes in a higher layer are considered.Consequently, for a combination codebook with N_(layer) layers, thenumber of searched codewords is

$M + {\sum\limits_{i = 1}^{N_{layer}}\; {N_{i}.}}$

Compared to a conventional codebook of the same size,

$M{\prod\limits_{i = 1}^{N_{layer}}\; N_{i}}$

codewords would be searched. Clearly, the codeword searching complexityis significantly reduced when combination codebooks are used.

Differential feedback is also supported by the hierarchical structure ofthe combination codebook. The nodes associated with a mother node in ahigher level will systematically have higher correlations and be nearerto each other in the vector space. This may readily facility thedifferential feedback and therefore reduces feedback overhead. Forexample, in a first feedback, an index to the base codebook of thecombination codebook is fed back. Then in a second feedback, an index toa first refinement of the localized codebook of the combination codebookis fed back instead of both the index of the base codebook and the indexof the first refinement of the localized codebook. In general, in anl-th feedback, an index to an (l−1)-th refinement of the localizedcodebook is fed back instead of a complete set of indices.

An exemplary combination codebook for a MIMO wireless communicationssystem with four transmit antennas is provided below:

${{Base}\mspace{14mu} {codebook}\text{:}\mspace{14mu} C_{base}^{4}} = {\frac{1}{2} \times \begin{bmatrix}{- 1} & {- 1} & j & {- j} \\j & j & {- 1} & 1 \\j & {- j} & {- 1} & {- 1} \\1 & {- 1} & {- j} & {- j}\end{bmatrix}}$${{Localized}\mspace{14mu} {codebook}\text{:}\mspace{14mu} C_{local}^{4}} = {\frac{1}{2} \times \begin{bmatrix}1 & 1 & 1 & 1 \\1 & {- j} & {- 1} & j \\1 & {- 1} & 1 & {- 1} \\1 & j & {- 1} & {- j}\end{bmatrix}}$${{Scaling}\mspace{14mu} {factor}\text{:}\mspace{14mu} \alpha} = \frac{\sqrt{2}}{4}$

Four-bit rank one combination codebook for four transmit antennas withthe CM property

C 16^(4, 1) = [c 16₁^(4, 1), c 16₂^(4, 1), …, c 16₁₆^(4, 1)]$\begin{matrix}\left\lbrack {{c\; 16_{1}^{4,1}},{c\; 16_{2}^{4,1}},} \right. \\\left. {{c\; 16_{3}^{4,1}},{c\; 16_{4}^{4,1}}} \right\rbrack\end{matrix} = \begin{pmatrix}{- 0.5} & {{- 0.5}j} & {{- 0.2151} - {0.4514j}} & {0.2151 + {0.4514j}} \\{- 0.5} & {0.1536 - {0.4758j}} & {{- 0.5}j} & {0.4758 - {0.1536j}} \\{{- 0.4514} - {0.2151j}} & {{- 0.2151} - {0.4514j}} & {{- 0.5}j} & 0.5 \\{{- 0.4758} + {0.1536j}} & {{- 0.5}j} & {0.1536 - {0.4758j}} & 0.5\end{pmatrix}$ $\begin{matrix}\left\lbrack {{c\; 16_{5}^{4,1}},{c\; 16_{6}^{4,1}},} \right. \\\left. {{c\; 16_{7}^{4,1}},{c\; 16_{8}^{4,1}}} \right\rbrack\end{matrix} = \begin{pmatrix}{- 0.5} & {{- 0.5}j} & {{- 0.2151} - {0.4514j}} & {0.4514 + {0.2151j}} \\{0.5j} & {{- 0.4758} - {0.1536j}} & {- 0.5} & {{- 0.1536} - {0.4578j}} \\{0.4514 + {0.2151j}} & {0.2151 + {0.4514j}} & {0.5j} & {- 0.5} \\{{- 0.1536} - {0.4758j}} & 0.5 & {0.4758 + {0.1536j}} & {0.5j}\end{pmatrix}$ $\begin{matrix}\left\lbrack {{c\; 16_{9}^{4,1}},{c\; 16_{10}^{4,1}},} \right. \\\left. {{c\; 16_{11}^{4,1}},{c\; 16_{12}^{4,1}}} \right\rbrack\end{matrix} = \begin{pmatrix}{- 0.5} & {{- 0.5}j} & {{- 0.2151} - {0.4514j}} & {0.4514 + {0.2151j}} \\0.5 & {{- 0.1536} + {0.4758j}} & {0.5j} & {{- 0.4758} + {0.1536j}} \\{{- 0.4514} - {0.2151j}} & {{- 0.2151} - {0.4514j}} & {{- 0.5}j} & 0.5 \\{0.4758 - {0.1536j}} & {0.5j} & {{- 0.1536} + {0.4758j}} & {- 0.5}\end{pmatrix}$ $\begin{matrix}\left\lbrack {{c\; 16_{13}^{4,1}},{c\; 16_{14}^{4,1}},} \right. \\\left. {{c\; 16_{15}^{4,1}},{c\; 16_{16}^{4,1}}} \right\rbrack\end{matrix} = \begin{pmatrix}{- 0.5} & {{- 0.5}j} & {{- 0.2151} - {0.4514j}} & {0.4514 + {0.2151j}} \\{{- 0.5}j} & {0.4578 + {0.1536j}} & 0.5 & {0.1536 + {0.4758j}} \\{0.4514 + {0.2151j}} & {0.2151 + {0.4514j}} & {0.5j} & {- 0.5} \\{0.1536 + {0.4758j}} & {- 0.5} & {{- 0.4758} - {0.1536j}} & {{- 0.5}j}\end{pmatrix}$

FIG. 7 illustrates a diagram of codeword searching for the combinationcodebook for a MIMO wireless communications system with four transmitantennas. The number of codewords searched is decreased by 50% from 16codewords down to eight (8) codewords.

Three-bit rank one combination codebook for four transmit antennas withthe CM property

C8^(4,2) =[c8₁ ^(4,2) , c ₂ ^(4,2) , . . . ,c8₁₆ ^(4,2)]

c8₁ ^(4, 2) c8₂ ^(4, 2) c8₃ ^(4, 2) c8₄ ^(4, 2) [c16₁ ⁴, c16₅ ⁴] [c16₂⁴, c16₆ ⁴] [c16₃ ⁴, c16₇ ⁴] [c16₄ ⁴, c16₈ ⁴] c8₅ ^(4, 2) c8₆ ^(4, 2) c8₇^(4, 2) c8₈ ^(4, 2) [c16₉ ⁴, c16₁₃ ⁴] [c16₁₀ ⁴, c16₁₄ ⁴] [c16₁₁ ⁴, c16₁₅⁴] [c16₁₂ ⁴, c16₁₆ ⁴]

Three-bit rank four combination codebook for four transmit antennas withthe CM property

C4^(4,4) =[c4₁ ^(4,4) ,c4₂ ^(4,4) , . . . ,c4₄ ^(4,4)]

c4₁ ^(4, 4) c4₂ ^(4, 4) c4₃ ^(4, 4) c4₄ ^(4, 4) [c8₁ ^(4, 2), c8₅^(4, 2)] [c8₂ ^(4, 2), c8₆ ^(4, 2)] [c8₃ ^(4, 2), c8₇ ^(4, 2)] [c8₄^(4, 2), c8₈ ^(4, 2)]

FIG. 8 a illustrates a data plot 800 of system throughput for a range ofsignal-to-noise ratios for several different codebooks for a MIMOcommunications system with four transmit antenna and two receive antennaand a first traffic model. A first trace 805 illustrates the performanceof a combination codebook as disclosed above, a second trace 810illustrates the performance of a DFT based codebook, and a third trace815 illustrates the performance of a Grassmannian link packing (GLP)based codebook. First trace 805 shows that the performance of thecombination codebook is superior to that of DFT- and GLP-based codebooksand is only exceeded by an ideal MIMO communications system with perfectchannel state information (shown as a fourth trace 820).

FIG. 8 b illustrates a data plot 850 of system throughput for a range ofsignal-to-noise ratios for several different codebooks for a MIMOcommunications system with four transmit antenna and two receive antennaand a second traffic model. A first trace 855 illustrates theperformance of a combination codebook as disclosed above, a second trace860 illustrates the performance of a GLP based codebook with a four bitindex, a third trace 865 illustrates the performance of a DFT basedcodebook with a four bit index, and a fourth trace 870 illustrates theperformance of a DFT based codebook with a three bit index. First trace855 shows that the performance of the combination codebook is similar tothat of GLP based codebooks with a four bit index and superior to eitherfour bit index or three bit index DFT based codebooks. Again, firsttrace 855 is surpassed by an ideal MIMO communications system withperfect channel state information (shown as a fifth trace 875).

An exemplary combination codebook for a MIMO wireless communicationssystem with two transmit antennas is provided below:

${{Base}\mspace{14mu} {codebook}\text{:}\mspace{14mu} C_{base}^{2}} = {\frac{\sqrt{2}}{2} \times \begin{bmatrix}1 & 1 & 1 & 1 \\^{\frac{\pi}{8}j} & ^{\frac{5\pi}{8}j} & ^{\frac{3\pi}{8}j} & ^{\frac{7\pi}{8}j}\end{bmatrix}}$${Localized}\mspace{14mu} {codebook}\text{:}\mspace{14mu} \begin{matrix}{C_{local}^{2} = {\frac{\sqrt{2}}{2} \times}} \\\begin{bmatrix}{1.3604 - {0.2706j}} & {1.3604 + {0.2706j}} \\{0.0538 + {0.2706j}} & {0.0538 - {0.2706j}}\end{bmatrix}\end{matrix}$${{Scaling}\mspace{14mu} {factor}\text{:}\mspace{14mu} \alpha} = \frac{\sqrt{2}}{2}$

Two-bit rank four combination codebook for two transmit antennas withthe CM property C8^(2,1)=[c8₁ ^(2,1), c8₂ ^(2,1) . . . , c8₈ ^(2,1)]

c8₁ ^(2,1) c8₂ ^(2,1) c8₃ ^(2,1) c8₄ ^(2,1) c8₅ ^(2,1) c8₆ ^(2,1) c8₇^(2,1) c8₈ ^(2,1) [1, 1]$\left\lbrack {1,e^{\frac{\pi}{4}j}} \right\rbrack$ [1, j]$\left\lbrack {1,e^{\frac{3\pi}{4}j}} \right\rbrack$ [1, −1]$\left\lbrack {1,e^{\frac{\pi}{4}j}} \right\rbrack$ [1, −j]$\left\lbrack {1,e^{\frac{3\pi}{4}j}} \right\rbrack$

Three-bit rank two combination codebook for two transmit antennas withthe CM property C4^(2,2)=[c4₁ ^(2,2), c4₂ ^(2,2), . . . , c4₄ ^(2,2)]

c4₁ ^(2, 2) c4₂ ^(2, 2) c4₃ ^(2, 2) c4₄ ^(2, 2) c8₁ ^(2, 1), c8₅ ^(2, 1)c8₂ ^(2, 1), c8₈ ^(2, 1) c8₃ ^(2, 1), c8₇ ^(2, 1) c8₄ ^(2, 1), c8₆^(2, 1)

FIG. 9 a illustrates a flow diagram of subscriber unit operations 900 ingenerating channel quality information feedback. Subscriber unitoperations 900 may begin with the estimating of the channel to produce achannel estimate (block 905). The estimating of the channel may beperformed by estimate channel block 255. After estimating the channel,the channel estimate may be quantized using a CM codebook (block 910).The channel estimate may also be normalized prior to being quantized.Then, an index of a codeword in the CM codebook may be transmitted to aBTS serving the subscriber unit. Subscriber unit operations 900 may thenterminate.

FIG. 9 b illustrates a flow diagram of subscriber unit operations 950 ingenerating channel quality information feedback. Subscriber unitoperations 950 may begin with the estimating of the channel to produce achannel estimate (block 955). The estimating of the channel may beperformed by estimate channel block 255. After estimating the channel,the channel estimate may be quantized using a CM base codebook (block957). This may produce an index to the CM base codebook. The channelestimate may be normalized prior to being quantized.

Then, a CM localized codebook may be scaled and rotated based on vectorc_(cnt) (block 959). The scaled and rotated CM localized codebook maythen be used to quantize the channel estimate (block 961). This mayproduce an index to the scaled/quantized CM localized codebook. Theindices (the index to the CM base codebook and the index to thescaled/quantized CM localized codebook) may be transmitted to a BTSserving the subscriber unit. Subscriber unit operations 900 may thenterminate.

Generally, the scaling and rotating of the CM localized codebook may beperformed multiple times, with each time adding to the refinement of thequantization of the channel estimate. Therefore, although the discussionfocuses on a single scaling and rotating of the CM localized codebook,subscriber unit operations 950 may be readily modified to performmultiple scaling/rotating operations on the CM localized codebook.

FIG. 10 a illustrates a flow diagram of BTS operations 1000 intransmitting information to a subscriber unit using channel qualityinformation feedback provided by the subscriber unit. BTS operations1000 may begin receiving channel quality information feedback (orfeedback bits) from a subscriber unit (block 1005). From the channelquality information feedback, a index to a CM codebook may be extracted(block 1007). The index to the CM codebook may be used to reconstruct achannel estimate vector (block 1009). The channel estimate vector may beused to adjust radio frequency (RF) hardware in the BTS (block 1011) andthe BTS may make use of the adjusted RF hardware to transmit to thesubscriber unit (block 1013). BTS operations 1000 may then terminate.

FIG. 10 b illustrates a flow diagram of BTS operations 1050 intransmitting information to a subscriber unit using channel qualityinformation feedback provided by the subscriber unit. BTS operations1050 may begin with the BTS receiving channel quality informationfeedback (or feedback bits) from a subscriber unit (block 1055). Fromthe channel quality information feedback, a index to a CM base codebookmay be extracted (block 1057). The index to the CM codebook may be usedto reconstruct a channel estimate vector (block 1059).

The BTS may also receive additional channel quality information feedbackfrom the subscriber unit (block 1061). From the channel qualityinformation feedback, an index to a CM localized codebook may beextracted (block 1063). The index to the CM localized codebook may beused in a scaling and rotating of the CM localized codebook (block 1065)and the reconstructed channel estimate vector may be refined using thescaled/rotated CM localized codebook (block 1067).

The additional channel quality information feedback may be a part of thesame channel quality feedback used to provide the index to the CMcodebook. Alternatively, the additional channel quality informationfeedback may be sent to the BTS in a different feedback transmission.

The refined channel estimate vector may be used to adjust radiofrequency (RF) hardware in the BTS (block 1069) and the BTS may make useof the adjusted RF hardware to transmit to the subscriber unit (block1071). BTS operations 1050 may then terminate.

Generally, the scaling and rotating of the CM localized codebook may beperformed multiple times. As the BTS continues to receive indices forthe CM localized codebook (in channel quality information feedbacktransmissions), the BTS may continue to refine the reconstructed channelestimate vector rather than starting over again with the CM basecodebook. Therefore, although the discussion focuses on a single scalingand rotating of the CM localized codebook, BTS operations 1050 may bereadily modified to perform multiple scaling/rotating operations on theCM localized codebook from the channel quality information feedback.

Although the embodiments and their advantages have been described indetail, it should be understood that various changes, substitutions andalterations can be made herein without departing from the spirit andscope of the invention as defined by the appended claims. Moreover, thescope of the present application is not intended to be limited to theparticular embodiments of the process, machine, manufacture, compositionof matter, means, methods and steps described in the specification. Asone of ordinary skill in the art will readily appreciate from thedisclosure of the present invention, processes, machines, manufacture,compositions of matter, means, methods, or steps, presently existing orlater to be developed, that perform substantially the same function orachieve substantially the same result as the corresponding embodimentsdescribed herein may be utilized according to the present invention.Accordingly, the appended claims are intended to include within theirscope such processes, machines, manufacture, compositions of matter,means, methods, or steps.

1. A method for operating in a communications network, the method comprising: receiving a codebook, the codebook comprising a plurality of codewords; determining if the codebook satisfies a constant modulus property; when the codebook does satisfy the constant modulus property, storing the codebook; when the codebook does not satisfy the constant modulus property, converting the codebook so that it satisfies the constant modulus property by, for each codeword in the codebook, dividing the codeword by the codeword's magnitude, and storing the codebook satisfying the constant modulus property; and causing to transmit a transmission to a communications device, wherein the transmission is encoded using a codeword in the stored codebook.
 2. The method of claim 1, wherein determining if the codebook satisfies the constant modulus property further comprises determining that the codebook satisfies the constant modulus property when $\left| c_{i,j} \right|^{2\;} = \frac{1}{N_{t}}$ for all i and j, where c_(i,j) is an i-th element of a j-th codeword in the codebook, |c_(i,j)| returns the magnitude of codeword c_(i,j), and N_(t) is a number of transmit antenna in the communications network.
 3. The method of claim 1, wherein determining if the codebook satisfies the constant modulus property further comprises determining that the codebook does not satisfy the constant modulus property when $\left| c_{i,j} \middle| {}_{2}{\neq \frac{1}{N_{t}}} \right.$ for any codeword in the codebook.
 4. The method of claim 1, wherein the codebook comprises a base codebook and a localized codebook, wherein the communications network is a multiple input, multiple output communications network with four transmit antennas, and wherein the base codebook is expressible as ${C_{base}^{4} = {\frac{1}{2} \times \begin{bmatrix} {- 1} & {- 1} & j & {- j} \\ j & j & {- 1} & 1 \\ j & {- j} & {- 1} & {- 1} \\ 1 & {- 1} & {- j} & {- j} \end{bmatrix}}},$ the localized codebook is expressible as ${C_{local}^{4} = {\frac{1}{2} \times \begin{bmatrix} 1 & 1 & 1 & 1 \\ 1 & {- j} & {- 1} & j \\ 1 & {- 1} & 1 & {- 1} \\ 1 & j & {- 1} & {- j} \end{bmatrix}}},$ a scaling factor is expressible as ${\alpha = \frac{\sqrt{2}}{4}},$ and a four-bit rank one codebook with a constant modulus property is expressible as C16^(4,1) =[c16₁ ^(4,1) ,c16₂ ^(4,1) , . . . ,c16₁₆ ^(4,1)], where $\left\lbrack {{c\; 16_{1}^{4,1}},{c\; 16_{2}^{4,1}},{c\; 16_{3}^{4,1}},{c\; 16_{4}^{4,1}}} \right\rbrack = {{\begin{pmatrix} {- 0.5} & {{- 0.5}j} & {{- 0.2151} - {0.4514j}} & {0.2151 + {0.4514j}} \\ {- 0.5} & {0.1536 - {0.4758j}} & {{- 0.5}j} & {0.4758 - {0.1536j}} \\ {{- 0.4514} - {0.2151j}} & {{- 0.2151} - {0.4514j}} & {{- 0.5}j} & 0.5 \\ {{- 0.4758} + {0.1536j}} & {{- 0.5}j} & {0.1536 - {0.4758j}} & 0.5 \end{pmatrix}\left\lbrack {{c\; 16_{5}^{4,1}},{c\; 16_{6}^{4,1}},{c\; 16_{7}^{4,1}},{c\; 16_{8}^{4,1}}} \right\rbrack} = {{\begin{pmatrix} {- 0.5} & {{- 0.5}j} & {{- 0.2151} - {0.4514j}} & {0.4514 + {0.2151j}} \\ {0.5j} & {{- 0.4758} - {0.1536j}} & {- 0.5} & {{- 0.1536} - {0.4578j}} \\ {0.4514 + {0.2151j}} & {0.2151 + {0.4514j}} & {0.5j} & {- 0.5} \\ {{- 0.1536} - {0.4758j}} & 0.5 & {0.4758 + {0.1536j}} & {0.5j} \end{pmatrix}\left\lbrack {{c\; 16_{9}^{4,1}},{c\; 16_{10}^{4,1}},{c\; 16_{11}^{4,1}},{c\; 16_{12}^{4,1}}} \right\rbrack} = \begin{pmatrix} {- 0.5} & {{- 0.5}j} & {{- 0.2151} - {0.4514j}} & {0.4514 + {0.2151j}} \\ 0.5 & {{- 0.1536} + {0.4758j}} & {0.5j} & {{- 0.4758} + {0.1536j}} \\ {{- 0.4514} - {0.2151j}} & {{- 0.2151} - {0.4514j}} & {{- 0.5}j} & 0.5 \\ {0.4758 - {0.1536j}} & {0.5j} & {{- 0.1536} + {0.4758j}} & {- 0.5} \end{pmatrix}}}$ ${{and}\left\lbrack {{c\; 16_{13}^{4,1}},{c\; 16_{14}^{4,1}},{c\; 16_{15}^{4,1}},{c\; 16_{16}^{4,1}}} \right\rbrack} = \begin{pmatrix} {- 0.5} & {{- 0.5}j} & {{- 0.2151} - {0.4514j}} & {0.4514 + {0.2151j}} \\ {{- 0.5}j} & {0.4578 + {0.1536j}} & 0.5 & {0.1536 + {0.4758j}} \\ {0.4514 + {0.2151j}} & {0.2151 + {0.4514j}} & {0.5j} & {- 0.5} \\ {0.1536 + {0.4758j}} & {- 0.5} & {{- 0.4758} - {0.1536j}} & {{- 0.5}j} \end{pmatrix}$
 5. The method of claim 1, wherein the codebook comprises a base codebook and a localized codebook, wherein the communications network is a multiple input, multiple output communications network with two transmit antennas, and wherein the base codebook is expressible as ${C_{base}^{2} = {\frac{\sqrt{2}}{2} \times \begin{bmatrix} 1 & 1 & 1 & 1 \\ ^{\frac{\pi}{8}j} & ^{\frac{5\pi}{8}j} & ^{\frac{3\pi}{8}j} & ^{\frac{7\pi}{8}j} \end{bmatrix}}},$ the localized codebook is expressible as ${C_{local}^{2} = {\frac{\sqrt{2}}{2} \times \begin{bmatrix} {1.3604 - {0.2706j}} & {1.3604 + {0.2706j}} \\ {0.0538 + {0.2706j}} & {0.0538 - {0.2706j}} \end{bmatrix}}},$ a scaling factor is expressible as ${\alpha = \frac{\sqrt{2}}{2}},$ and a two-bit rank four combination codebook for two transmit antennas with the constant modulus property is expressible as C8^(2,1) =[c8₁ ^(2,1) ,c8₂ ^(2,1) . . . ,c8₈ ^(2,1)], where ${{c\; 8_{1}^{2,1}} = \left\lbrack {1,1} \right\rbrack},{{c\; 8_{2}^{2,1}} = \left\lbrack {1,^{\frac{\pi}{4}j}} \right\rbrack},{{c\; 8_{3}^{2,1}} = \left\lbrack {1,j} \right\rbrack},{{c\; 8_{4}^{2,1}} = \left\lbrack {1,^{\frac{3\pi}{4}j}} \right\rbrack},{{c\; 8_{5}^{2,1}} = \left\lbrack {1,{- 1}} \right\rbrack},{{c\; 8_{6}^{2,1}} = \left\lbrack {1,^{{- \frac{\pi}{4}}j}} \right\rbrack},{{c\; 8_{7}^{2,1}} = \left\lbrack {1,{- j}} \right\rbrack},{{{and}\mspace{14mu} c\; 8_{8}^{2,1}} = {\left\lbrack {1,^{{- \frac{3\pi}{4}}j}} \right\rbrack.}}$
 6. The method of claim 1, wherein the method is for subscriber unit operation, wherein the communications device is a base station, and wherein the causing to transmit comprises: computing an estimate of a communications channel between the subscriber unit and the base station; quantizing the estimate with the stored codebook; and transmitting information based on the quantized estimate to the base station.
 7. The method of claim 6, further comprising: adjusting a localized codebook based on the quantized estimate; and re-quantizing the quantized estimate with the adjusted localized codebook, thereby producing a refined channel estimate.
 8. The method of claim 7, wherein the transmitting the information is further based on the refined channel estimate.
 9. The method of claim 7, wherein the adjusting the localized codebook comprises scaling the localized codebook.
 10. The method of claim 9, wherein the scaling the localized codebook comprises scaling codewords in the localized codebook with a scaling factor.
 11. The method of claim 9, wherein the adjusting the localized codebook further comprises rotating the localized codebook.
 12. The method of claim 11, wherein the rotating the localized codebook comprises: finding a rotation matrix; and multiplying the localized codebook with the rotation matrix.
 13. The method of claim 7, wherein the localized codebook satisfies the constant modulus property.
 14. The method of claim 1, wherein the method is for base station operation, wherein the communications device is a subscriber unit, and wherein the method further comprises: receiving channel information from the subscriber unit; extracting a codebook index from the channel information; and reconstructing a channel estimate using the codebook index and the stored codebook, wherein the transmission is precoded using the reconstructed channel estimate.
 15. The method of claim 14, further comprising: extracting a localized codebook index from the channel information; adjusting a localized codebook based on the codebook index; and further reconstructing the channel estimate using the localized codebook index and the adjusted localized codebook.
 16. The method of claim 15, wherein the localized codebook satisfies the constant modulus property.
 17. The method of claim 15, wherein the adjusting the localized codebook comprises: scaling the localized codebook based on the codebook index; and rotating the localized codebook based on the codebook index.
 18. The method of claim 14, wherein the causing to transmit comprises: adjusting transmission circuitry in the base station using the reconstructed channel estimate; precoding the transmission with the reconstructed channel estimate; and transmitting the precoded transmission to the subscriber unit.
 19. The method of claim 14, further comprising: receiving a refinement channel information from the subscriber unit; extracting a refinement localized codebook index from the refinement channel information; adjusting a localized codebook based on the codebook index; and further reconstructing the channel estimate using the refinement localized codebook index and the adjusted localized codebook.
 20. The method of claim 19, wherein the refinement channel information and the channel information are received by the base station in different feedback transmissions. 